Asymptotic properties of the derivative of self-intersection local time of fractional Brownian motion

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• 作者：Arturo Jaramillo ; ^jagil@ku.edu ; David Nualart
• 关键词：60G22 ; 60F05
• 刊名：Stochastic Processes and their Applications
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：127
• 期：2
• 页码：669-700
• 全文大小：427 K
• 卷排序：127

文摘

Let {Bt}t≥0{Bt}t≥0 be a fractional Brownian motion with Hurst parameter 23<H<1. We prove that the approximation of the derivative of self-intersection local time, defined as αε=∫0T∫0tpε′(Bt−Bs)dsdt, where pε(x)pε(x) is the heat kernel, satisfies a central limit theorem when renormalized by ε32−1H. We prove as well that for q≥2q≥2, the qqth chaotic component of αεαε converges in L2L2 when 23<H<34, and satisfies a central limit theorem when renormalized by a multiplicative factor ε1−34H in the case 34<H<4q−34q−2.